Fitzpatrick told the two media outlets that he had reported a fellow senior union organiser to police for allegedly issuing him a death threat. He said the threat came after Fitzpatrick raised concerns about the relationship between union figures and a businessman who received a contract at Barangaroo in Sydney. The ABC and Fairfax Media said the businessman had links to crime figures and a history of owing workers money.

Fitzpatrick said he received a call last year: “You've gone too far this time, you fat cunt. You're dead, you're fucking dead. Don't care how many police you've got. I'm coming out tomorrow and you are fucking dead. Bang.”

Fitzpatrick later identified a CFMEU colleague as the caller.

The CFMEU national secretary, Dave Noonan, told the ABC the other official strenuously denied making the death threats. Noonan responded to the earlier reports by saying the union was examining the specific allegations but anyone with evidence of criminal conduct should go to the police.

A senior union figure offered Fitzpatrick $300,000 in members' money to leave the union quietly but instead he resigned with a year's pay late last year, the ABC reported.

The justice minister, Michael Keenan, said the Australian Crime Commission was working with Victoria police, NSW police and the NSW Crime Commission "to investigate organised crime links in the building and construction industry".

The earlier reports – which allege participation by criminals in construction projects, and implicate some union officials in NSW and Victoria in improper conduct – have renewed political debate about the Abbott government’s push to reintroduce the Australian Building and Construction Commission (ABCC). The claims have also led to speculation the government will broaden a planned judicial inquiry into union “slush funds”.

The prime minister, Tony Abbott, said the allegations showed the need to bring back a “tough cop on the beat” to stamp out a culture of lawlessness in the industry.

But Labor – which can join with the Greens to block bills until the new Senate takes effect in July – reaffirmed its opposition to the ABCC, which would have coercive powers.

The opposition stressed the need for police investigation of claims of criminal conduct rather than introducing “another layer of bureaucracy”.

Likewise, the Greens denounced the ABCC as a body that undermined people’s rights at work. It was introduced by the Howard government but abolished by the subsequent Labor government, which replaced it with the Fair Work Building and Construction inspectorate.